查询词典 proved

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

Results indicated that aphids fed on fresh bamboos by aggregately distributing, and their predators in bamboo forests were separately collected in different parts, main of which were in accord with negative binomial distribution and Polya-Eggenberger distribution, it was proved that some natural enemies in some sample sites were spraying extensively from single plot to around places, the population density of bamboo aphids was proved to be stable in a regular time.

在竹林中主要符合负二项式分布和 P-E 核心分布，为不均匀的聚集分布，存在由点片向四周扩散的现象，频次分析和聚集度指标的分析结果基本一致，其中瓢虫的聚集程度不及另外2种天敌的明显。

There are series of papers studying the solvability of an incompressible, viscous, instationary fluid contained in a domian bounded entirely by a free surface. In 1977, Solonnikov proved its local solvability in a Holder space for any initial date but without surface tension. In 1984, he considered the same problem in a Sobolev space with surface tension being taken into account. In I992, Mogilevskii and Solonnikov treated the same problem in a Holder space, where the coefficient of surface tension is not a constant. There are also short-time existence results for the solvability of an incompressible, vicous, unsteady fluid bounded above by a free surface and below by a fixed bottom which approach horizontal planes at infinity. In 1981, Beale proved its local solvability in a Sobolev space for any initial date but without surface tension. In 1983, Allain were concerned with the same problem in R〓 with surface tension but under the assumption that the initial fluid domain was near a horizontal strip. In 1987, he obtained the same result without the preceding assumption. In 1996, Tani solved the same problem in R with surface tension. For the solvability of an incompressible viscous instationary fluid in Ω R bounded inside by a free surface S and outside by a rotating boundary S, in 1995 Ciuperca proved its local existence in a Sobolev space for any initial date but without surface tension. In this paper, we consider the same problem with surface tension.

对于边界完全是由自由边界组成的有界区域中粘性不可压流体的非定常运动问题，Solonnikcv于1977年在忽略表面张力情况下证明了初值问题小时间解在Holder空间的存在性，于1984年在有表面张力情况下证明了初值问题问题小时间解在Sobolev空间的存在性，Mogilevskii和Solonnikov于1992年在表面张力系数可以不是常数情况下证明了初值问题小时间解在Holder空间的存在性；对于上面是自由边界、下面是固定边界且两边界在无限处趋于水平的无限区域中粘性不可压流体的非定常运动问题，Beale于1981年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性，Allain于1983年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性，但其中假定初始区域近似是个水平条，他于1987年去掉了这个假定得到同样的结果，Tani于1996年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性；对于R中内面是自由边界、外面是旋转边界S的有界区域中粘性不可压流体的非定常运动问题，Ciuperca于1995年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性，本文考虑了在有表面张力情况下初值问题可解性问题。

Decision rule chain and distance function of decision rule are proposed, by which the order of decision rules are explained. The group scale's effect on decision quality and the marginal contribution of decision-makers are analyzed. It's pointed out that the increase of the scale will enhance the decision quality with the optimal decision rule applied. Otherwise it is likely to weaken the decision quality. It's proved that for homogeneous group with simple majority rule applied the marginal contribution of decision-maker will decrease while the scale increases or the decisional competencies of other decision-makers increase; 3.We study the group decision-making with a leader in it. It's proved that the existence of the leader impairs the decision quality when the group applies the optimal decision rule.

研究了决策者的决策能力不确定情况下的群体决策，给出了最优决策规则，指出其仍然是广义加权多数规则；提出了决策规则链和决策规则距离函数的概念，利用这些概念解释了群体决策规则的序现象；分析了群体规模对决策质量的影响、决策者决策能力的边际贡献，指出当群体应用最优规则时，群体规模的增大会提高决策质量，否则群体规模的增大可能会削弱决策质量；证明了对于应用简单多数规则的同质群体，随着其规模的增大，决策者决策能力对决策质量的边际贡献会减小；随着其他决策者决策能力的提高，决策者决策能力对决策质量的边际贡献也会减小； 3。

The completeness and soundness theorem of this resolution principle are also proved; Secondly, a α-resolution method which can be used to judge that a lattice-valued logic formula is always α-false (i. e. is always less than α) is established, in which the completeness and soundness theorem are also proved.

进一步，类似于经典情形下寻求判定一个公式恒真的半可判定算法，建立了判定基于格蕴涵代数的格值逻辑中一类格值公式在一定真值水平α下恒假的α-归结方法，并证明了其可靠性和完备性。

Rough ideals been first introduced by Kuroki N. Under the condition of the congruence relation, a rough set of a subsemigroup was proved to be its subsemigroup, while that of a leftideal was also proved to be its leftideal.

Kuroki N研究了半群中的粗理想，首次提出了粗子半群和粗理想的概念，证明了在同余关系下，半群的粗糙集是半群，左理想的粗糙集是左理想。

At the same time, some properties of rough Set in quotient ring are given and proved. The fifth chapter is Rough Primary Ideals and Rough Fuzzy Primary Ideals in Semigroups, the concept of rough primary ideals and fuzzy rough primary ideals in semigroups are introduced. Under the condition of the complete congruence relation, a rough set of a primary ideal in semigroups is proved to be its primary ideal.

同时，在商环中讨论了粗糙集的一些性质，并给出这些结论的严格证明；第五章是半群中的粗准素理想和粗模糊准素理想，首次提出了半群中的粗准素理想与粗模糊准素理想的概念，证明了在完备同余关系下，半群中准素理想的粗糙集是准素理想。

To the problem of unbiasedness of L 1 estimation,basing on uniqueness of solution,Zhou Shijiang proved it according to dual theorem of linear programming; and Wang Zhizhong proved it according to probability statistics theorem by using the method from special to general; also,basing on error distribution theorem and probability statistics theorem,the authors proved it.

对于L1 估计的无偏性问题，周世健基于解法的惟一性，根据线性规划的对偶理论，证明了L1 估计的无偏性[5] ；王志忠根据数理统计理论，采用由特殊情形推广到一般情形的方法，证明了L1 估计的无偏性[6] 。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

The evolutionary relationships were investgated by comparing the results from molecular data alone or molecular data combined morphological characters using different analysis methods: maximum parsimony by PAUP(superscript *) 4.0 and Bayesian inference by MrBayes 3.0B4. Base composition and ti/tv of 28S rDNA D2 regions were analyzed by PAUP(superscript *) 4.0. The results showed that GC content of the 28S rDNA D2 gene sequences of subfamily Euphorinae ranges from 40.00% to 49.25%. Transversion frequency of sequence variable sites among species of Euphorinae was higher than that of transition. The subfamily Euphorinae was proved to be a paraphyletic group with close relationship to subfamilies Neoneurinae and Cenocoelinae; only two tribes, Meterorini and Microctonini, were proved to be monophyletic groups; Centistini, Cosmophorini, Euphorini and Dinocampini were paraphyletic groups; the basal position of tribe Meterorini within Euphorinae was partially supported by our phylogenetic trees, and tribe Microctonini was proved to be a group at the top of the trees.

结果表明：优茧蜂亚科的28S rDNA D2基因序列片段的GC%含量在40.00%~49.25%之间变动，而对于碱基替代情况来讲，优茧蜂亚科各个成员间序列变异位点上颠换大于转换；不同的分析和算法所产生的系统发育树都表明目前根据形态定义出的优茧蜂亚科Euphorinae不是一个单系群，而是一个与蚁茧蜂亚科Neoneurinae和高腹茧蜂亚科Cenocoelinae混杂在一起的并系群；在优茧蜂亚科内部，悬茧蜂族Meterorini和食甲茧蜂族Microctonini（排除猎户茧蜂属Orionis）为单系群，而宽鞘茧蜂族Centistini、大颚茧蜂族Cosmophorini、优茧蜂族Euphorini、瓢虫茧蜂族Dinocampini为并系群；悬茧蜂族Meterorini在优茧蜂亚科Euphorinae内位于基部位置的观点得到部分的支持，同时食甲茧蜂族Microctonini被判定为相对进化的类群。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失